Theory of Elementary Particles

弦理论最近最重要的发展之一是发现了AdS/CFT对应两边的可积性。Nepomechie的主要目标是应用技术的可积量子自旋链和可积量子场论，他帮助开发在过去的二十年中，问题的弦/规范理论。他已经对精确的体散射矩阵和边界散射矩阵的理解做出了贡献，他计划利用这些矩阵来获得进一步的精确结果。阿尔瓦雷斯将进行量子场论和弦理论的研究。阿尔瓦雷斯正在研究扩展的椭圆属家庭的Dirac-拉蒙德运营商。Atiyah和Singer关于Dirac算子的族指数定理可以用于规范理论中，以研究破坏理论量子化的反常现象。弦理论中的类似物应该是狄拉克-雷蒙算子的族指数定理。即使我们并不真正知道什么是弦理论，这个族指数定理应该给我们一些关于微扰论之外的理论结构的信息。这是试图了解弦论非微扰方面的重要尝试。这项研究的更广泛的影响如下：这项工作可能会在弦理论，数学以及凝聚态物理学和统计力学中开辟新的方向。阿尔瓦雷斯和内波米奇都将帮助为下一代美国公民提供科学培训，特别是那些来自迈阿密拉丁裔社区的人。他们的研究结果将通过互联网和科学出版物以及通过研讨会和国际会议传播。PI还在当地公立学校举办科学讲座。

One of the most important recent developments in string theory is the discovery of integrability on both sides of the AdS/CFT correspondence. Nepomechie's main objective is to apply techniques of integrable quantum spin chains and integrable quantum field theories, which he has helped develop during the past two decades, to problems in string/gauge theory. He has already contributed to the understanding of exact bulk and boundary scattering matrices, which he plans to exploit to obtain further exact results. Alvarez will conduct research in quantum field theory and string theory. Alvarez is studying the extension of the elliptic genus to families of Dirac-Ramond operators. The families index theorem of Atiyah and Singer for the Dirac operator can be used in gauge theories to study the anomalies that spoil the quantization of the theory. The analog in string theory should be a families index theorem for the Dirac-Ramond operator. Even though we do not really know what is string theory, this families index theorem should give us some information about the structure of the theory beyond perturbation theory. This is an important attempt at trying to learn about non-perturbative aspects of string theory. The broader impacts of this research are as follows: this work may open new directions in string theory, mathematics, as well as condensed matter physics and statistical mechanics. Both Alvarez and Nepomechie will help provide scientific training to the next generation of American citizens, in particular to those from the Latino community in Miami. Their findings will be disseminated through the internet and scientific publications, as well as through seminars and international conferences. The PIs also give lectures at local public schools on science.